A090377 Number of configurations that require a minimum of n moves to be reached, starting with the empty square in one of the corners of an infinitely large extension of Sam Loyd's sliding block 15-puzzle.

1, 2, 4, 10, 26, 66, 173, 456, 1230, 3318, 9066, 24768, 68304, 188370, 523083, 1452560, 4054708, 11318926

Offset: 0

Author

Hugo Pfoertner, Nov 27 2003

Keywords

• more
• nonn

Comments

The first n terms of this sequence coincide with the first n terms of the corresponding sequences for n X n sliding block puzzles (see Cross-references).

Crossrefs

Cf. A089473 (3 X 3 puzzle), A089484 (4 X 4), A090031 (5 X 5), A090032 (6 X 6).

Programs

Python

# uses alst(), swap() in A089473
nn = 13
start = "".join([chr(i) for i in range(45, 45+(nn+1)**2)]) # chr(45) is "-"
print(alst(start, (nn+1, nn+1), maxd=nn)) # Michael S. Branicky, Jan 02 2021

Extensions

a(10)-a(17) from Michael S. Branicky, Dec 28 2020